Question: A local gift shop sold bags of candy and cookies for Halloween. Bags of candy cost $$7.50$, and bags of cookies cost $$3.50$, and sales equaled $$65.00$ in total. There were $6$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the gift shop.
Solution: Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${7.5x+3.5y = 65}$ ${y = x+6}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+6}$ for $y$ in the first equation. ${7.5x + 3.5}{(x+6)}{= 65}$ Simplify and solve for $x$ $ 7.5x+3.5x + 21 = 65 $ $ 11x+21 = 65 $ $ 11x = 44 $ $ x = \dfrac{44}{11} $ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $ {y = x+6}$ to find $y$ ${y = }{(4)}{ + 6}$ ${y = 10}$ You can also plug ${x = 4}$ into $ {7.5x+3.5y = 65}$ and get the same answer for $y$ ${7.5}{(4)}{ + 3.5y = 65}$ ${y = 10}$ $4$ bags of candy and $10$ bags of cookies were sold.